Power and Pin Efficient Chip-to-Chip Communications with Common-Mode Rejection and SSO Resilience

ABSTRACT

In bus communications methods and apparatus, a first set of physical signals representing the information to be conveyed over the bus is provided, and mapped to a codeword of a spherical code, wherein a codeword is representable as a vector of a plurality of components and the bus uses at least as many signal lines as components of the vector that are used, mapping the codeword to a second set of physical signals, wherein components of the second set of physical signals can have values from a set of component values having at least three distinct values for at least one component, and providing the second set of physical signals for transmission over the data bus in a physical form.

CROSS REFERENCES

This application is a Continuation of U.S. patent application Ser. No.12/982,777 now U.S. Pat. No. 8,539,318 entitled “Power and Pin EfficientChip-to-Chip Communications with Common-Mode Rejection and SSOResilience” filed Dec. 30, 2010, which is a non-provisional applicationclaiming priority to U.S. Provisional Patent Application No. 61/351,845entitled “Error Control Coding for Differential Signaling” filed Jun. 4,2010 naming Harm Cronie and Amin Shokrollahi (referred to herein as“Cronie II”), all of which are incorporated herein by reference.

The following prior applications are herein incorporated by reference intheir entirety for all purposes: U.S. patent application Ser. No.12/784,414 filed May 20, 2010 naming Harm Cronie and Amin Shokrollahiand entitled “Orthogonal Differential Vector Signaling” (referred toherein as “Cronie I”);

The following references are cited in this application using the labelsset out in brackets:

[Slepian] Slepian, D., “Permutation Modulation”, Proceedings of theIEEE, Vol. 53, No. 3, pp. 228-236 (March 1965);

[Cornelius] U.S. Pat. No. 6,661,355 to William Cornelius and WilliamAlthas entitled “Methods and Apparatus for Constant-Weight Encoding &Decoding” (2003);

[Stan-Burelson] Stan, M., and Burelson, W., “Bus-Invert Coding forLow-power I/O”, IEEE Transactions on VLSI systems, Vol. 3, No. 1, pp.49-50 (March 1995); and

[Tallini] Tallini, L., and Bose, B., “Transmission Time Analysis for theParallel Asynchronous Communication Scheme”, IEEE Transactions onComputers, Vol. 52, No. 5, pp. 558-571 (2003).

FIELD OF THE INVENTION

The present invention relates to communications in general and inparticular to transmission of signals capable of conveying informationbetween integrated circuits.

BACKGROUND OF THE INVENTION

When an electronic device contains more than one integrated circuit(“IC”), signals typically need to be conveyed from chip to chip over acommunication bus. Communication may also take place over acommunication bus between two ICs that are part of two differentdevices. In either case, the communication bus might comprise one ormore wires. The ICs might be mounted on a printed circuit board (“PCB”)with the wires being striplines or microstrips. For communicationbetween devices or boards, the wires might be the copper wires of acable or optical fibers connecting the devices/boards. As is well known,the communication requires electrical energy and can generate electricalnoise and errors can occur when the conditions of communication are notideal.

For an increasing number of applications, the speed of the communicationbus is a limiting factor. One way to increase the speed is to increasethe number of wires that make up the bus. However, this also increasesthe number of pins of the ICs that are needed and many times, IC pinsare a scarce resource. Another limiting factor is the power consumptionof the bus and the circuitry driving the bus. Simply increasing thetransmit power might not result in a better performance of the bus,because that might increase the amount of noise and lower performance.

Signals transmitted on a communication bus are subjected to severaltypes of noise. One source of noise is thermal noise that can be modeledas independent Gaussian noise. The resilience against Gaussian noise canbe improved by increasing signal swings or by the use of well-designedsignaling schemes. Another type of noise is interference that may resultfrom neighboring wires of the communication bus. Some noise andinterference has a component that is common to the several wires of thebus and this noise is called common-mode noise. Another source of noiseis simultaneous switching output (“SSO”) noise that is caused by a busdriver current that varies in time. SSO noise can cause major problemsin modem high-speed bus communication systems. Yet another source ofnoise is crosstalk noise, which is caused by interference of the signalson the different wires of the same bus. Crosstalk noise is one of themain sources of noise for high-frequency buses and is hard to eliminateby just increasing the energy of the signals on the bus, since anincrease of energy leads directly to an increase of interference tonearby wires on the bus, and will lead to even worse crosstalk noise.

There are several approaches to signaling for chip-to-chipcommunications that may address one or more of the above constraints.

One approach is single-ended signaling where an information-carryingsignal is transmitted on a single wire with respect to a commonreference. Although single-ended signaling is efficient in terms of thenumber of wires used, it is susceptible to common-mode noise and itintroduces SSO noise. Furthermore, for the detection of a single-endedsignal, a reference is required at the receiver. Inaccuracies in thegeneration of the reference signal lead to higher error rates of thecommunication system. Hence, a signaling method that does not require areference is preferred over a signaling method that does require one.Single-ended signaling is also not very efficient in terms oftransmission power that is required to achieve certain Gaussian noiseresilience, and it is also not efficient in terms of crosstalk noise.

Another signaling method is differential signaling. In differentialsignaling, an information-carrying signal is transmitted on a pair ofwires. The original information-carrying signal is encoded into thedifference between the signals transmitted on the pair of wires. Theadvantage of differential signaling is that it rejects noise that iscommon on both wires.

For chip-to-chip communications, the information-carrying signal isoften a non-return-to-zero (“NRZ”) encoded signal and, as such,differential signaling does not introduce SSO. Another advantage is thatdifferential signaling is less sensitive to interference and crosstalk.The reason for this is interference and crosstalk mainly couple into thecommon mode and are cancelled at the receiver. Moreover, in terms ofresilience against Gaussian noise, differential signaling is morepower-efficient compared to single-ended signaling. The maindisadvantage of differential signaling is that it uses twice the numberof pins compared to differential signaling.

The ratio between the number of bits transmitted in a cycle of time Tand the number of bus wires is referred to as the pin efficiency of thebus. While communication buses based on differential signaling providegood noise resilience, their pin efficiency is low. Differentialsignaling is more power efficient than single-ended signaling but stilla substantial amount of the power consumption of a bus communicationsystem is used in the drivers of the bus wires.

One approach to addressing this issue is explained in Cronie I, whichdescribes a method for bus communication that achieves a higherpin-efficiency than differential signaling while using less transmitpower and provides resilience to common-mode noise and SSO noise. Oneapproach described therein, referred to as “Orthogonal DifferentialVector Signaling” or “ODVS”, achieves a pin-efficiency that is close toone when the number of wires is large. In some applications, it ispreferable to increase the noise resilience of a communication system asdescribed above at the expense of the pin-efficiency.

Cronie II teaches a method referred to as “Coded Differential VectorSignaling” or “COVECS” that uses methods of forward error correction touse some of the pins saved by ODVS to increase the noise resilience.

While the methods of Cronie I and Cronie II offer substantialimprovements regarding the tradeoff of pin-efficiency and noiseresilience as compared to other approaches, there are some applicationswherein additional improvements are possible. For example, sinceembodiments of ODVS might use a number of wires that are a power of two,applications where that is not a convenient number of wires might needanother approach.

With the methods of Cronie II, improving the noise resilience of thesystem might use up a significant number of pins saved by ODVS and thecircuitry needed for encoding and decoding according to the teachings ofCronie II may be complex and may not be applicable in situations wherethe data transfer is of very high rate, thus requiring another approach.

Another application is where the pin-efficiency needs to exceed one.What is needed is a method that provides a wider range of possible pairsof pin-efficiency and noise resilience, allows for very efficientencoding and decoding, and leads to new tradeoffs between pin-efficiencyand noise resilience.

BRIEF SUMMARY OF THE INVENTION

In methods and apparatus for bus communications according to aspects ofthe present invention, a first set of physical signals representing theinformation to be conveyed over the bus is provided, and mapped to acodeword of a spherical code, wherein a codeword is representable as avector of a plurality of components and the bus uses at least as manysignal lines as components of the vector that are used, mapping thecodeword to a second set of physical signals, wherein components of thesecond set of physical signals can have values from a set of componentvalues having at least three distinct values for at least one component,and providing the second set of physical signals for transmission overthe data bus in a physical form.

In an specific embodiment, the spherical code is a sparse permutationmodulation code and the operation of mapping the first set of physicalsignals to a codeword of the permutation modulation code furthercomprises accessing a storage location for a generating vector,selecting a distinguished position of the generating vector of thepermutation modulation code, mapping the first set of physical signalsto a first sequence of bits, subdividing the first sequence of bits intoa second sequence of bits and a third sequence of bits, comparing thesecond sequence and the third sequence and putting a first predeterminedvalue into the distinguished position of the generating vector if thesecond sequence and third sequence satisfy a predetermined relation, andputting a second predetermined value into a second position of thegenerating vector different from the distinguished position, wherein thesecond position is obtained from the second sequence using apredetermined process, when the second sequence and third sequence donot satisfy the predetermined relation, putting a first predeterminedvalue into a first position of the generating vector obtained from thesecond sequence, and putting a second predetermined value into a secondposition of the generating vector obtained from the third sequence, andputting a third predetermined value into all the positions of thegenerating vector that are not equal to the first position or the secondposition.

The following detailed description together with the accompanyingdrawings will provide a better understanding of the nature andadvantages of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an environment in which the present invention mightbe used.

FIG. 2 is a schematic diagram illustrating the communication bus of FIG.1 in greater detail.

FIG. 3 is a schematic diagram illustrating the environment of FIG. 1wherein a vector signal encoder and a vector signal decoder are used.

FIG. 4 is a signal plot illustrating a signaling scheme that might beused on the bus lines of FIG. 3.

FIG. 5 is a block diagram illustrating the vector signal decoder of FIG.3 in greater detail.

FIG. 6 is a block diagram illustrating the vector signal encoder of FIG.3 in greater detail.

FIG. 7 is a block diagram illustrating functionality of the code mapunit of FIG. 6.

FIG. 8 is a block diagram illustrating functionality of an alternativecode map unit that can be used in the vector signal encoder of FIG. 6.

FIG. 9 provides examples of spherical codes as might be used by the codemap unit of FIG. 7; FIG. 9 a gives an example of spherical codes inthree dimensions and size 8; FIG. 9 b gives an example of sphericalcodes in three dimensions and size 16.

FIG. 10 is a block diagram illustrating functionality of the transformunit of FIG. 6.

FIG. 11 is an illustration of an example Hadamard matrix that might beused by the transport unit of FIG. 10.

FIG. 12 is a block diagram illustrating an embodiment of the vectorsignal encoder of FIG. 3 in greater detail.

FIG. 13 is a flowchart of an example encoding process for encoding inputbits into a vector signal that can be used on the communication bus.

FIG. 14 is a flowchart of another example encoding process for encodinginput bits into a vector signal that can be used on the communicationbus.

FIG. 15 is a flowchart of an example of a lower pin-efficiency encodingprocess for encoding input bits into a vector signal that can be used onthe communication bus.

FIG. 16 is a flowchart of another example of a lower pin-efficiencyencoding process for encoding input bits into a vector signal that canbe used on the communication bus.

FIG. 17 is a flowchart illustrating an encoding process for a PM code.

FIG. 18 is a chart of values that might be stored in memory or generatedin various steps of the process illustrated in FIG. 17, for variousexample inputs.

FIG. 19 is a flowchart illustrating a demodulating process for a PMcode.

FIG. 20 is a flowchart illustrating a decoding process for a PM code.

FIG. 21 is a table of values that might occur during the decodingprocess of FIG. 20.

FIG. 22 illustrates an encoding procedure for sparse PM codes; in theprocedure of FIG. 22 a, the number n is not a power of 2, and m ischosen such that 2 m−1<n<2 m; in the procedure of FIG. 22 b, the numbern is a power of 2 and m is chosen such that n=2 m+1.

FIG. 23 illustrates a decoding procedure for sparse PM codes, whereinthe number n is assumed to not be a power of 2, and m is chosen suchthat 2 m−1<n<2 m.

FIG. 24 illustrates a decoding procedure for sparse PM codes, whereinthe number n is assumed to be a power of 2, and m is chosen such thatn=2 m+1.

FIG. 25 is a table of values that might be used for sparse PM coding.

FIG. 26 is a block diagram illustrating an embodiment of the vectorsignal encoder of FIG. 3 that uses multilevel PM codes.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 illustrates an environment in which the present invention mightbe used. As illustrated there, an information source 110 provides asequence of k information symbols periodically, at an interval of Tseconds, for example. Without loss of generality, assume that theseinformation symbols are bits. These bits are to be transmitted by a bustransmitter 120 over a communication bus 130 to a bus receiver 140 at adestination 150. The communication bus 130 comprises n physical wires135.

In the case where the n physical wires are easily allowed for and thetransmission of k/Tn bits per second on each wire does not create noiseproblems, no special circuit would be needed—each T seconds, k/n bitscould be placed on a wire and sent from source to destination. However,there are many cases where the number of physical wires needs to be keptlow and/or simply transmitting whatever bits are present at the sourcewould cause noise sufficient to introduce errors for the values of k/Tthat are needed for the particular use.

Examples of communication bus 130 might include a bus between aprocessor and memory, wherein the physical wires take the form ofstriplines or microstrips on a printed circuit board (“PCB”) and theprocessor is the source for some information bits (while the memory isthe destination) and the memory is the source for other information bits(while the processor is the destination). Another example of acommunication bus 130 is a set of wires connecting two devices.Generally, the methods disclosed herein are applicable for a widevariety of communication buses. Some buses operate using electricalsignals that are added to the wires by controlling voltage changes,whereas others are added to the wires by controlling current changes,and in yet others, the wires conduct light (and possibly notelectricity) and the signals are optical signals imposed on opticalfibers or other light-conducting medium. Striplines and microstripstypically operate with electrical signals.

In operation, the information bits of source 110 are fed to a bustransmitter 120, which has the task of transforming those bits into aset of physical signals that can be transmitted on bus 130. At the otherend of bus 130, bus receiver 140 maps the received signals back toinformation bits for use at destination 150.

FIG. 2 is a schematic diagram illustrating communication bus 130 ingreater detail. As illustrated there, bus 130 comprises l wires 220. Bustransmitter 120 generates a set of n waveforms 240, which are labeledx_(i)(t) to x_(n)(t) (and collectively as x(t)) and can representvoltage signals, current signals and/or optical signals. In thisexample, n is some integer greater than 5, but it should be understoodthat it could be four, eight, 64, 256 or some integer that is not awhole power of two, for example three. The waveforms 250 that arereceived at bus receiver 140 might not be exactly the same as waveforms240, due to shifting of signals, amplification, shifting, noise andother effects. The received signals are labeled herein as y₁(t) toy_(n)(t) (and collectively as y(t)). The main task of the bus receiveris to recover the original information bits based on the waveforms y₁(t)to y_(n)(t). To facilitate this process, the bus transmitter 120 and thebus receiver 140 may perform several tasks such as amplification,filtering, demodulation, synchronization, equalization, and bustermination.

Noise Effects

As explained herein, there are novel techniques described here foraddressing issues of common-mode noise rejection, resilience against SSOnoise, resilience against Gaussian noise, and favorable properties withrespect to crosstalk noise.

Common-mode Noise: Where there is a noise signal that disturbs x(t) suchthat each wire is affected in the same way, the received signals mightbe represented as y_(i)(t)=x_(i)(t)+c(t), for i=1, 2, . . . , n, wherec(t) denotes the common-mode noise signal. Of course, it is assumed thatthe bus receiver does not exactly know c(t).

SSO Noise: Simultaneous Switching Output (“SSO” noise) is typicallycaused when the circuitry that drives the bus wires has a powerconsumption that varies over time. The instantaneous power consumption,P(t), of driver circuitry is typically proportional to the sum of thesquares of the amplitudes of the signals on each individual wire.

Model of Vector Signal Encoder that Addresses Common-Mode and SSO Noise

As explained elsewhere herein, a vector signal encoder that obtains someof information bits to be conveyed and generates a signal for aplurality of lines, i.e., a “vector signal”, can often providecommon-mode noise resilience by having the sum of the components of thevector signal sum to zero, i.e., by satisfying Equation 1.

Σ_(i=1) ^(n) x _(i)(t)=0  (Eqn. 1)

Where the vector signal might contribute to SSO noise, this can bereduced by maintaining a constant total power consumption of the busdrivers, which can be expressed as shown in Equation 2, wherein P₀ is aconstant related to the energy of the signals.

Σ_(i=1) ^(n) x _(i) ²(t)=P ₀  (Eqn. 2)

Example Vector Signal Encoder

FIG. 3 is a schematic diagram illustrating use of a vector signalencoder and a vector signal decoder. Bus transmitter 120 might include avector signal encoder 310 and a bus driver 320, while bus receiver 140might include a vector signal decoder 340 and a bus receiver 330. Vectorsignal encoder 310 preferably encodes the information provided by source110 such that Equations 1 and 2 hold.

In one example, vector signal encoder 310 uses a form of vector pulseamplitude modulation, wherein a basic pulse shape, p(t), with a finiteduration of T seconds is defined and the amplitude of this pulse ismodulated according to a signaling scheme. Two examples of pulse shapesare shown in FIG. 4. The left hand-side of FIG. 4 shows a rectangularpulse 410 of duration T. Pulse 410 is often used as an approximation formodeling purposes. A more practical pulse 420 is shown in the righthand-side of FIG. 4. Pulse 420 has a finite rise time, t_(r). In onepreferred embodiment, vector signal encoder 310 generates a signal,x_(i)(t)=c_(i)p(t), for each i-th symbol period of duration T, wherec_(i) is a real number defining the pulse for that symbol period.Herein, the label “c” refers to a vector containing the c_(i) values andthe set of all possible such c is denoted by C. Herein, the set C isreferred to as the signal constellation. In embodiments where this formof pulse amplitude modulation is used, Equation 1 and Equation 2 reduceto Equation 3 and Equation 4, respectively.

Σ_(i=1) ^(n) c _(i)=0  (Eqn. 3)

Σ_(i=1) ^(n) c _(i) ² =P ₀  (Eqn. 4)

FIG. 5 illustrates an example of a vector signal decoder 340 thatincorporates a common-mode cancellation unit 510, and effectivelysatisfies Equation 1. A set of signals 520 enters vector signal decoder340 and an adder 530 computes their sum. The sum is fed to a set ofsubtractors 540 (which can be differential circuits) that “subtract” thesum signal (or a proportion of the sum signal) from each of the signals520 entering the vector signal decoder. As a result, common-mode noiseis cancelled if it is common on the entire width of the bus.

In addition to common-mode noise and SSO noise, which can be addressedby particular circuits, there is also Gaussian noise, which isindependently added to the signals on the bus, and externalinterference, which is added to the signals that traverse the bus. A buscan be made resilient to those types of noise, as explained herein, byproper selection of the signaling on the bus. As is known, resiliencecan be obtained by ensuring that the possible values of the vector chave a large Euclidean distance from one other. To that end, vectorsignal decoder 340 may include an additional processing unit 550 thatdecodes the set of received signals to the corresponding originalinformation bits, while having signal constellations, C, with a goodminimal distance while satisfying Equation 1 and 2.

One preferred embodiment of a vector signal encoder 310 is exemplifiedin FIG. 6. The input to vector signal encoder 310 is a sequence of ksource bits that are to be transmitted on the bus with l wires in a timeinterval of T seconds. The vector signal encoder 310 may include a codemap unit 610, a transform unit 620 and a modulator 630.

Code map unit 610 takes the k source bits as its input and generates nvalues, which can be either real or complex numbers, such that the sumof the squares of the absolute values of these numbers is a givenconstant, or belongs to a small set of possible values.

Transform unit 620 takes as its input the n values from the code mapunit and transforms these values to another set of n values, where thetransformation is as explained further below. Modulator 630 modulatesthe output of transform unit 620 to create the signals for the buslines. An example might be pulse amplitude modulation according to apredefined pulse shape, p(t), that results in signals corresponding tox₁(t) to x_(n)(t), which are sent to bus driver 320 to be transmitted onthe bus.

The values sent on the bus are carefully chosen so as to maximize orincrease their robustness to various types of noise as described above.This can be accomplished by a proper choice of code map unit 610 andtransform unit 620. For example, code map unit 610 may generate thevalues in such a way that the vectors generated have good mutualdistance properties with respect to Euclidean distance so as to provideresilience against Gaussian and thermal noise. Furthermore, code mapunit 610 may be configured to ensure that every vector is of equalEuclidean norm so that Equation 2 is satisfied. Transform unit 620 maybe such that after the transform, the mutual distance properties of theinput vectors are preserved and Equation 1 is satisfied.

Examples and preferred embodiments of code map unit 610 and transformunit 620 will now be described, with reference to FIGS. 7-12.

Code Map Unit

An example code map unit is shown in FIG. 7, comprising a mechanism toapply a generator matrix, G, of a binary error-correcting code to thevector of input bits, s, from the source to obtain a vector of bits c,as set out in Equation 5.

c=Gs  (Eqn. 5)

The resulting vector c is provided to unit 720, which applies a map, ƒ,to the individual components of the vector c. There are many choices forsuch a map, and depending on the underlying application, one choice maybe preferred over another.

For example, if the signals transmitted on communication bus 130 belongto the set {−1, +1}, then the map ƒ might be defined by ƒ(x)=(−1)^(x)for a bit x. If communication bus 130 allows for transmission of signalsbelonging to a set of size larger than two, the map ƒ may have adifferent form; for example, it could take pairs of bits and map them toone of the elements of a predefined set of four elements, or it may taketriples of bits and map them to one of the elements of a predefined setof eight elements, etc. Where ƒ is of the form above, the output ofvector signal encoder 610 is a vector v that is given by v=ƒ(c) whereinƒ(c) is understood as the vector for which the i-th entry is theapplication of ƒ to the i-th entry of c. Upon straightforwardcalculation, it should be apparent that the components of v satisfyEquation 2 with a value of P₀ being equal to the number of entries ofthe vector c. Furthermore, there are ample of possibilities to choose Gsuch that the resulting vectors have good mutual distance properties. Anexample of a matrix G for k=4 and n=7 is shown by Equation 6, whichhappens to the generator matrix of the binary [7,4,3] Hamming code.Other options are possible.

$\begin{matrix}{G = \begin{bmatrix}1 & 0 & 0 & 0 & 0 & 1 & 1 \\0 & 1 & 0 & 0 & 1 & 0 & 1 \\0 & 0 & 1 & 0 & 1 & 1 & 0 \\0 & 0 & 0 & 1 & 1 & 1 & 1\end{bmatrix}} & \left( {{Eqn}.\mspace{14mu} 6} \right)\end{matrix}$

In general, if the generator matrix of a code of length n, dimension k,and minimum Hamming distance d is used, then the minimum Euclideandistance between any two distinct vectors generated by signal encoder610 is twice the square root of the Hamming distance, whereas the energy(i.e., Euclidean norm) of every vector generated is the square root ofn, and thus the ratio between the minimum distance and the Euclideannorm of the generated vectors is as shown in Equation 7.

$\begin{matrix}{2\sqrt{\frac{d}{n}}} & \left( {{Eqn}.\mspace{14mu} 7} \right)\end{matrix}$

Therefore, if a small minimum distance is desired, then the chosen codeshould have a large minimum Hamming distance compared to n.

FIG. 8 is a block diagram illustrating functionality of an alternativecode map unit that can be used in the vector signal encoder. Itcomprises a spherical code unit 820 and a spherical encoder L. Thevector of input bits is given to spherical encoder 810 which, based onthe input vector and the spherical code 820, outputs one of the elementsof the spherical code. As is known to those of skill in the art, aspherical code is a finite set of vectors of equal norm in then-dimensional Euclidean space. Often, it is required that the minimumEuclidean distance between the elements of the spherical code is large,so that small perturbations of said elements do not result in confusionof one for another. There are many examples of spherical codes known tothose of skill in the art. For example, the four vertices of a regulartetrahedron on the unit sphere in three dimensions is a spherical codegiven by Equation 8. The minimum Euclidean distance between thesevectors is the square root of 8, which is considered to be very large.

$\begin{matrix}{{Vertices} = \left\{ {{\frac{1}{\sqrt{3}}\left( {1,1,1} \right)},{\frac{1}{\sqrt{3}}\left( {{- 1},1,{- 1}} \right)},{\frac{1}{\sqrt{3}}\left( {1,{- 1},{- 1}} \right)},{\frac{1}{\sqrt{3}}\left( {{- 1},{- 1},1} \right)}} \right\}} & \left( {{Eqn}.\mspace{14mu} 8} \right)\end{matrix}$

FIGS. 9 a and 9 b give further examples of spherical codes in dimension3 of sizes 8 and 16, respectively. The elements in FIG. 9 a all havenorm approximately equal to 1.16342285. Those in FIG. 9 b have normapproximately equal to 0.942858. These spherical codes have a propertythat the minimum Euclidean distance between the vectors is rather large.These spherical codes are well-known to researchers in fields related tothe transmission of information on noisy channels, such as wirelesscommunication, satellite communication, communication on a modem line,and the like. Other spherical codes are possible.

When using spherical codes in applications, a process needs todetermine, for every given vector of bits that is used, a unique elementof the spherical code associated with that particular vector of bits.Herein “spherical code encoding process” is used to refer to thatprocess.

Spherical coding is a general case of the encoding performed by theencoder of FIG. 7. In that case, the possible outputs of the function ƒform a spherical code. In the situation of FIG. 7, the spherical codeencoding process uses an encoding process for the underlying code. Incase of general spherical codes, the encoding process can be moreelaborate and may depend on the particular spherical code used. Such aprocedure might comprise a table matching every possible array of bitsof a specified length with one of the elements of the spherical code.For example, for the regular tetrahedron above, the mapping could be asshown in Table 1 (where “s” represents the square root of three).

TABLE 1 Input Bits Vector 00 [1, 1, 1]/s 01 [−1, 1, −1]/s 10 [1, −1,−1]/s 11 [−1, −1, 1]/s

Using the teachings herein, tables can be created for other sphericalcodes (such as those illustrated by FIGS. 9 a and 9 b) as well. One ofthe disadvantages of some encoding methods is the amount of memory theyuse, for storing an indication of an element of the spherical code foreach possible sequence of input bits. Where the number of elements inthe spherical code is small, for example, 4, 8, or 16, such an encodingmethod may be possible to use without sacrificing resources such asarea, storage, or speed. In other cases, it may be prudent to usespherical codes that are equipped with fast encoders, and also fastdecoders. Permutation modulation codes, as described below, provide sucha class and may be used in embodiments of bus systems according to thepresent invention.

Differential Signaling, Single-Ended Signaling, and Spherical Codes

Differential signaling and single-ended signaling are known and can beviewed as special cases of signaling using spherical codes, as explainedbelow. In the case of single ended signaling on n wires, the signalstransmitted on these wires are of the form (a₁, . . . , a_(l)) where theentries of this vector can independently take on one of two possiblevalues. The set of such elements constitutes a spherical code accordingto the definitions above, and herein this particular spherical code isreferred to as a “hypercube” code.

In the case of differential signaling on 2 n wires, the signalstransmitted on these wires are of the form (a₁, −a₁, a₂, −a₂, . . . ,a_(n), −a_(n)) where each of the entries a_(j) is an element from a set{b, −b}. The set of such elements constitutes a spherical code accordingto the definitions above, and herein this particular spherical code isreferred to as a “reflected hypercube” code.

The Transform Unit

An example transform unit is given in FIG. 10. Transform unit 620 maycomprise circuits or elements that perform a transform defined by amatrix T. The matrix T may have the property that its columns are all ofEuclidean norm one, and are mutually orthogonal, and that the sum of therows of the matrix has substantially more zeros than non-zeroes, such asat least as many zeroes as non-zeroes, or at least two or three or moretimes as many zeroes. For example, the matrix T may have the propertythat the sum of its rows is zero in all coordinate positions exceptpossibly the first. Cronie I contains examples of such matrices. Oneclass of examples is furnished by Hadamard matrices. An example of sucha matrix is given in FIG. 11.

If the matrix T has the property that the sum of its rows is zero in allexcept possibly in the first position, then in one embodiment, thetransform unit 620 may form a vector, v′, from the vector v as shown byEquation 9.

$\begin{matrix}{v^{\prime}\begin{bmatrix}0 \\v_{1} \\\vdots \\v_{n - 1}\end{bmatrix}} & \left( {{Eqn}.\mspace{14mu} 9} \right)\end{matrix}$

In this embodiment, the transform unit 620 will apply the matrix Tdirectly to v′ to obtain x₁(t) to x_(n)(t).

Combined Code Map Unit and Transform Unit

In several cases, the combination of a binary-error correcting code oran appropriate spherical code with a transform leads to a signalconstellation wherein each vector is a permutation of some base vectorx₀. As an example, consider a vector signal encoder that employs thebinary [7, 4, 3] Hamming code for its code map unit, and employs theHadamard matrix of size 8 of FIG. 11 for its transform unit. The codemap unit and the transform unit define the signal set that is shown FIG.12. The resulting signal vectors are permutations of the vectors [−7, 1,1, 1, 1, 1, 1, 1] and −[−7, 1, 1, 1, 1, 1, 1, 1].

A spherical code for which all the elements are permutations of a singlebase element is called a “permutation modulation code.” These codes areexplained further in [Slepian] and since they are known, some details ofthem need not be described herein. Thus, the Hamming code and theHadamard transform described above define a permutation modulation code.In one embodiment, the code map unit and the transform unit are combinedinto a single permutation encoder 1210, as shown in FIG. 12. In theexample above, permutation encoder 1210 may apply the map shown in Table2 to generate a signal vector from a set of four bits.

TABLE 2 Input Bits Vector in R^(n) 0000 [−7, 1, 1, 1, 1, 1, 1, 1] 0001[1, −7, 1, 1, 1, 1, 1, 1] 0010 [1, 1, −7, 1, 1, 1, 1, 1] 0011 [1, 1, 1,−7, 1, 1, 1, 1] 0100 [1, 1, 1, 1, −7, 1, 1, 1] 0101 [1, 1, 1, 1, 1, −7,1, 1] 0110 [1, 1, 1, 1, 1, 1, −7, 1] 0111 [1, 1, 1, 1, 1, 1, 1, −7] 1000−[−7, 1, 1, 1, 1, 1, 1, 1] 1001 −[1, −7, 1, 1, 1, 1, 1, 1] 1010 −[1, 1,−7, 1, 1, 1, 1, 1] 1011 −[1, 1, 1, −7, 1, 1, 1, 1] 1100 −[1, 1, 1, 1,−7, 1, 1, 1] 1101 −[1, 1, 1, 1, 1, −7, 1, 1] 1110 −[1, 1, 1, 1, 1, 1,−7, 1] 1111 −[1, 1, 1, 1, 1, 1, 1, −7]

A process for performing this encoding efficiently is shown in FIG. 13.There, the input bits x[0], x[1], x[2], x[3] are read in (from memory orsome other input) (step 1310). In step 1320, a variable s is calculatedwhere s=−1 if x[0]=1, and s=0 otherwise. Thereafter, an index t iscalculated in step 1330. This index is a number between 0 and 7, and itsbit-representation is given by (x[1], x[2], x[3]). In step 1340, theentry with index t of the output vector is set to −7, and all otherindices are set to one. Finally, in step 1350 the vector s*(v[0], v[1],. . . , v[7]) is returned.

In yet another embodiment, the code vector signal encoder may employ acode map unit defined by the vertices of the tetrahedron and a Hadamardtransform of size 4. This combination results in a permutationmodulation code where the elements of x₀=[−3, 1, 1, 1] are permutedbased on the input bits. In an embodiment, the permutation encoder 1210may generate the signal vectors directly by mapping pairs of bits tosignal vectors as defined in Table 3.

TABLE 3 Input Bits Vector in R^(n) 00 [−3, 1, 1, 1] 01 [1, −3, 1, 1] 10[1, 1, −3, 1] 11 [1, 1, 1, −3]

A process for performing this encoding efficiently is shown in FIG. 14.There, the input bits x[0], x[1] are provided to the process in step1410. In step 1420, an index t is calculated that is a number between 0and 3, and has a bit-representation given by (x[0], x[1]). In step 1430,the entry with index t of the output vector is set to −3, and all otherindices are set to one. Finally, in step 1440, the vector (v[0], v[1],v[2], v[3]) is returned.

The two examples given above lead to coded vector signaling methods witha pin-efficiency of 0.5. Other similar coded vector signaling methodscan be obtained using this procedure, albeit at the expense of a lowerpin-efficiency. Such a procedure is described with reference to FIGS. 15and 16. The input 1510 to the process in FIG. 15 is a sequence of n bitsdenoted x[0], . . . , x[n−1]. In step 1520, these bits are interpretedas the binary expansion of an integer t and this integer is calculated.In step 1530, the entry t of the output vector v is set to the value−2^(n)+1 and all other values are set to 1. This vector is output instep 1540. The pin-efficiency of this procedure is n/2^(n). For n=2,this leads to the tetrahedron map of FIG. 14 with a pin-efficiency of0.5.

The input to the process in FIG. 16 is a sequence of n+1 bits denotedx[0], . . . , x[n]. In step 1620, a variable s is calculated where s=−1if x[0]=1, and s=1 otherwise. In step 1630, the sequence x[1], x[2], . .. , x[n] is interpreted as the binary expansion of an integer t, andthis integer is calculated. In step 1640, the entry t of the outputvector v is set to the value −(2^(n))+1 and all other values are setto 1. This vector is output in step 1650. The pin-efficiency of thisprocedure is (n+1)/2^(n). For n=3, this leads to the Hamming map of FIG.13 with a pin-efficiency of 0.5.

In specific applications, the vectors of the spherical code obtained maybe multiplied with the same scaling factor that accounts for thetransmit energy of the signals. The output of the processes in FIGS.13-16 may therefore, in certain applications, undergo a further step inwhich all the entries of the output vector are multiplied by a commonconstant value.

Permutation Modulation Codes

The use of a code map unit and the transform unit leads to severalsignal sets that satisfy Equation 1 and 2. Furthermore, these signalsets have a good noise performance. Several of these schemes result inpermutation modulation codes. As mentioned above, a permutationmodulation code (hereinafter “PM code” for short) is a spherical code inwhich all elements are permutations of a basic vector x₀. The basicvector x₀ is called the “generator” of the PM code, and the PM code issaid to be generated by x₀. Because of this property, Equation 2 aboveis always satisfied for the elements of a PM code. Moreover, the sum ofthe coordinates of x₀ is 0, then Equation 1 above is also alwayssatisfied for the elements of a PM code. In preferred embodiments, thevector x₀ has the shape shown in Equation 10, where n₀, n₁, . . . ,n_(t) are positive integers summing up to the number n of coordinates ofx₀, and where a₀, a₁, . . . , a_(t) are real numbers a₀>a₁> . . . >a_(t)such that Equation 11 is satisfied.

$\begin{matrix}{x_{0} = \left( \underset{\underset{n_{0}}{}}{a_{0},\ldots \mspace{14mu},a_{0}} \middle| {\underset{\underset{n_{1}}{}}{a_{1},\ldots \mspace{14mu},a_{1}}{\mspace{14mu} \ldots \mspace{14mu} }\underset{\underset{n_{t}}{}}{a_{t},\ldots \mspace{14mu},a_{t}}} \right)} & \left( {{Eqn}.\mspace{14mu} 10} \right) \\{{{n_{0}a_{0}} + {n_{1}a_{1}}},{{{+ \ldots} + {n_{t}a_{t}}} = 0}} & \left( {{Eqn}.\mspace{14mu} 11} \right)\end{matrix}$

It should be apparent from reading this disclosure that the elements ofthe PM code generated by x₀ can be enumerated by the differentpartitions of the set {1, 2, . . . , n} into subsets of sizes n₀, n₁, .. . , n_(t). Therefore, the PM code generated by x₀ has n!/(n₀!n₁! . . .n_(t)!) elements.

The encoding procedure for a PM code described in this way is quitesimple and will be described with reference to FIGS. 17 and 18. Forconvenience of the presentation, the function mult(n; n₀, n₁, . . . ,n_(t)) is defined to be equal to n!/(n₀!n1! . . . n_(t)!) if none of then_(i) is negative, and equal to zero if at least one of the n_(i) isequal to zero. Given a sequence x[0], . . . , x[m] of bits such that mis smaller than or equal to the binary logarithm of mult(n; n₀, n₁, . .. , n_(t)), the encoding of this sequence starts by interpreting the bitsequence as the binary representation of an integer l as l=x[0]+2x[1]+ .. . +2^(m)x[m]. The inputs to the procedure described in FIG. 17 are theinteger l to be encoded, and the integers n₀, n₁, . . . , n_(t). Theadditional input n is redundant as it is the sum of n₀, n₁, . . . ,n_(t). However, it has been added as an input for simplifying thepresentation. The output of the procedure in FIG. 18 is a set of flagsFLAG[0], FLAG[1], . . . , FLAG[n−1]. The interpretation of this outputis as follows: The i-th element of the vector is equal to a_(s) wheres=FLAG[i].

In step 1710, a variable, e, is set to zero. In step 1720, a decision ismade as to whether n is still positive or not. If not, then the processstops at step 1730 and outputs the values FLAG[0], FLAG[1], . . . ,FLAG[n−1]. If n is still positive, then in step 1740, the quantities A₀,. . . , A_(t) are calculated using the function mult( ) described above.Thereafter, in step 1750, an integer i in the set {0, 1, . . . , t-1} isfound such that the expression of Equation 12 is satisfied.

A ₀ +A ₁ + . . . +A _(i-1) ≦l≦A ₀ +A ₁ + . . . +A _(i)  (Eqn. 12)

Then, in step 1755, the flag FLAG[e] is set to i, and the counter e isincremented by 1. In step 1760, the value of l is reduced by A₀+A₁+ . .. +A_(i-1), that of n and n_(i) by one. At this point, the process goesback to step 1720 again.

An example of the procedure in FIG. 17 is now described with referenceto FIG. 18. In this example, the input to the procedure is given byl=198, n=8, n₀=2, n₁=4, and n₂=2. In every row of FIG. 18, the values ofthe variables l, n, n₀, n₁, n₂, e, and FLAG[e] are given at the end ofstep 1755 of FIG. 17. The output is the FLAG vector (1, 1, 1, 0, 1, 0,2, 2), corresponding to the element (a₁, a₁, a₁, a₀, a₁, a₀, a₂, a₂).

A demodulator for a PM code implements a procedure that maps a givenelement of the PM code to its corresponding bit-representation, whereinthe corresponding bit-representation is the sequence of bits which, uponusing the procedure of FIG. 17, yield the subset.

A demodulator for PM codes is now described with reference to FIG. 19.The input to this process, given in step 1905, are the integers n, n₀,n₁, . . . , n_(t), and the vector FLAG for which FLAG[e] is the index ofthe subset to which coordinate position e belongs. The output of thisprocess is an integer l greater than or equal to zero, and smaller thanmult(n; n₀, n₁, . . . , n_(t)). In step 1910, a counter, e, is set tozero, as is the current value of the variable l. In step 1920, adecision is made as to whether n is still positive. If not, then theprocess stops at step 1930 and outputs the value l. If n is stillpositive, then in step 1940, the quantities A₀, . . . , A_(t) arecalculated using the function mult( ) described above. Thereafter, instep 1950, the integer i is set to the value of FLAG[e] and l isincremented by A₀+A₁+ . . . +A_(i-1). In step 1960, the values of n andof n_(i) are reduced by one and the value of the counter e isincremented by one. At this point, the process returns to step 1920.

Decoding PM Codes

One reason for using PM codes is the existence of a simple procedure fordecoding elements of such codes when they are subjected to various typesof noise. A decoding process for PM codes is now described withreference to FIG. 20. The input to this process, shown in step 2005, isa vector (y₀, y₁, . . . , y_(n−1)) of real numbers. In some embodiments,this vector may be what has been received by unit 140 of FIG. 1 aftertransmission of an element of a PM code on the wires 135. In suchembodiments, this vector constitutes a perturbed version of the elementof the PM code that was sent by transmitter 120. The task of thedecoding process in FIG. 20 is to determine the bit-representation ofthe transmitted element wherein the bit-representation of the element isthe representation giving rise to the input l of the process in FIG. 17.

As used herein, it should be understood that when a decoding process orother process is performed or has a task, that performance or task isperformed by hardware circuits, by software executed by asspecial-purpose or general purpose processor, but that in the case ofsmall, fast circuits, the process is likely performed by special purposehardware elements. Not all of the elements of each possible hardwareelement are shown or described herein. In many cases, once thefunctionality of a process or elements are fully described,implementation in hardware is straightforward for circuits designers.

In step 2010 of the decoding process in FIG. 20, the elements y₀, y₁, .. . , y_(n−1) are sorted, and a permutation, pi, of the set {0, 1, . . ., n−1} is obtained such that Equation 13 is satisfied.

y _(pi(0)) ≧y _(pi(1)) ≧ . . . ≧y _(pi(n−1))  (Eqn. 13)

Thereafter, in step 2020, a vector FLAG comprising n entries isobtained, wherein Equations 14(0)-14(t) are satisfied.

$\begin{matrix}{\mspace{79mu} {{{FLAG}\left\lbrack {{pi}(0)} \right\rbrack} = {\ldots = {{{FLAG}\left\lbrack {{pi}\left( {n_{0} - 1} \right)} \right\rbrack} = 0}}}} & \left( {{{Eqn}.\mspace{14mu} 14}(0)} \right) \\{\mspace{79mu} {{{FLAG}\left\lbrack {{pi}\left( n_{0} \right)} \right\rbrack} = {\ldots = {{{FLAG}\left\lbrack {{pi}\left( {n_{0} + n_{1} - 1} \right)} \right\rbrack} = 1}}}} & \left( {{{Eqn}.\mspace{14mu} 14}(1)} \right) \\{\mspace{79mu} \ldots} & \; \\{{{FLAG}\left\lbrack {{pi}\left( {n_{0} + n_{1} + \ldots + n_{t - 1}} \right)} \right\rbrack} = {\ldots = {{{FLAG}\left\lbrack {{pi}\left( {n - 1} \right)} \right\rbrack} = t}}} & \left( {{{Eqn}.\mspace{14mu} 14}(t)} \right)\end{matrix}$

In step 2030, this vector FLAG is used to recover an integer l. Theprocedure for recovering l is in similar to the procedure in FIG. 19.The output of process of FIG. 20 is the binary representation of l.

Optimized PM Codes

It is straightforward to calculate the probability of error of theprocess in FIG. 20 under the assumption that the individual entries ofthe PM code element transmitted on the wires 135 are subjected toGaussian noise of mean 0 and a given variance. Based on suchcalculation, a best basic vector corresponding to a given value of t canbe determined. The table in FIG. 21 gives some of these optimized PMcodes. Other examples are possible, with values of t=3 or other valuesof t. In these examples the basic vector x₀ is of the form shown inEquation 15.

$\begin{matrix}{x_{0} = \left( {\underset{\underset{n_{0}}{}}{a,\ldots \mspace{14mu},a},\underset{\underset{n_{1}}{}}{{a - \delta},\ldots \mspace{14mu},{a - \delta}},\underset{\underset{n_{2}}{}}{{a - {2\delta}},\ldots \mspace{14mu},{a - {2\delta}}},\underset{n_{3}}{\underset{}{{a - {t\; \delta}},\ldots \mspace{14mu},{a - {t\; \delta}}}}} \right)} & \left( {{Eqn}.\mspace{14mu} 15} \right)\end{matrix}$

The first entry in the table is the vector [n₀, n₁, n₂, n₃]. The secondand the third entries are the numbers δ and α, respectively. The fourthentry is the number of bits that can be transmitted with this PM code,and the fifth entry is equal to the number n (which is the sum of n₀,n₁, n₂, n₃). In selected embodiments, this is the number of wires 135.The last column in the table is the power improvement in dB compared todifferential signaling of the same number of bits (over possibly alarger number of wires).

As can be seen from these examples, it is possible to use PM codes thatlead to pin-efficiencies that are much larger than the pin-efficiency ofdifferential signaling (which is 0.5) and are more power efficient. Forexample, it is possible to transmit 6 bits over 8 wires and use onlyroughly 70% of the energy required for sending the same number of bitsusing differential signaling. This method can be combined with alowering of the transmission speed per wire to obtain a transmissionthat has the same throughput as differential signaling, but usessignificantly less energy. Alternatively, by increasing the transmissionspeed per wire, it is possible to obtain a transmission that is fasterthan differential signaling by a factor of 2, and uses roughly the sameenergy. Another example is the transmission of 12 bits on 12 wires. Thisscheme has the same pin-efficiency as single ended signaling, but usesless than half the energy of the latter. Yet another example is the lastentry of the table. Here, it is possible to transmit 25 bits on 16wires, hence achieving a pin-efficiency of 25/16, or 1.5625. Thecorresponding transmission scheme would use less than half the energy ofsingle ended signaling, which achieves a pin-efficiency of 1.0.

Many other examples can be found upon reading this disclosure that leadto even higher pin-efficiencies and yet are more energy efficient thanthe single ended signaling method.

Sparse PM Codes

In a variety of applications, it is beneficial to have a PM codegenerated by a sparse vector, i.e., by a vector containing many zeroes.For example, where the vector is of length n but has only d non-zeroentries, wherein d is smaller than n, only d of the wires need to bedriven at any point in time, and hence the total current or voltage usedcould be significantly reduced. For example, if the basic vector hasonly two nonzero coordinates, and these are equal to some real number aand its negative −a, a procedure similar to differential signaling couldbe used to drive the voltages through the two wires corresponding tothese nonzero positions. Using the corresponding PM code would enabletransmission of about 2*lg(n) many bits, where lg(n) is the binarylogarithm of n. For values of n that are not too large, the number ofvoltage carrying (and hence energy consuming) wires is significantlyreduced with respect to differential signaling, while keeping thepin-efficiency to at least 0.5.

Another reason for using sparse PM codes in some embodiments is to dealwith crosstalk. This source of noise appears when information istransmitted on a bus at very high frequencies and is the primary sourceof noise at such frequencies. For sparse PM codes, crosstalk typicallyleads to the erroneous excitation of wires that carry zero voltage.Often, this excitation appears as Gaussian noise when decoding thesignals. Since the PM code is designed to have good resistance againstsuch noise, sparse PM codes typically show good robustness againstcrosstalk.

For these reasons, benefits are obtained with an encoding procedure anda decoding procedure for sparse PM codes that are simpler and requireless computational resources than the procedures outlined in FIG. 17 andin FIG. 19.

Such a method is now disclosed with reference to FIGS. 22-24. In thecase of FIG. 22 a, the number n is not a power of 2, and m is chosensuch that 2^(m−1)<n<2^(m). The input to this process are two vectors ofm bits each, called x and y. The output is a vector v that has only twononzero coordinates with values a and −a. In step 2210, the bits of xand y are used to obtain two indices i and j in the set {0, 1, . . . ,2^(m−1)}. Next, in step 2220, it is checked whether i and j are equal.If so, then v[i] is set to a, and v[2^(m)] to −a. Otherwise, v[i] is setto a, and v[j] to −a. All other entries of v are zero because of theinitialization in step 2210.

In the case of FIG. 22 b, the number n is a power of 2 equal to 2^(m+1).The input to this process are two vectors x and y of lengths m+1 and m,respectively. In step 2245, two indices i and j are calculated whosebit-representations are x and y, respectively. In addition, the outputvector v is initialized to all zeros. In step 2250, the process testswhether i=j. If so, then v[i] is set to a, whereas v[2^(m−1)] is set to−a. If the test in step 2250 is negative, then v[i] is set to a, andv[j] to −a.

The decoding procedures are exemplified in FIGS. 23 and 24. Similar tothe situation in FIG. 22 a, in FIG. 23 the number n is assumed to not bea power of 2, and the number m is such that 2^(m−1)<n<2^(m). The inputto the process in FIG. 23 is a vector (z₀, z₁, . . . , z_(n−1)) of realnumbers. In some embodiments, this vector may be what has been receivedby unit 140 of FIG. 1 after transmission of an element of a PM code onthe wires 135. In such embodiments, this vector constitutes a perturbedversion of the element of the PM code that was sent by transmitter 120.The task of the process in FIG. 23 is to determine thebit-representation of the transmitted element. In step 2310, two indicesi and j are determined such that z_(i) and z_(j) are the maximum and theminimum element among z₀, z₁, . . . , z_(n−1), respectively. Inaddition, the bit representations of these indices are also determinedand stored in vectors x and y as shown. In step 2315, it is checkedwhether j is bigger than 2^(m−1). If so, then there is a decoding error,and the process halts in step 2320, possibly by flagging an error. Ifthe test in step 2315 is negative, then step 2325 checks whether jequals 2^(m−1). If so, then the vector (x₀, . . . , x_(m−1), x₀, . . . ,x_(m−1)) comprising 2 m bits is output in step 2320. If the test in step2325 is negative, then the vector (x₀, . . . , x_(m−1), y₀, . . . ,y_(m−1)) is output.

In the situation of FIG. 24, the number n is assumed to be a power of 2,and the number m is such that n=2^(m+1). The input to the process inthis figure is the same as the input to the process in FIG. 23. In step2410, two indices i and j are determined such that z_(i) and z_(j) arethe maximum and the minimum element among z₀, z₁, . . . , z_(n−1),respectively. In addition, the bit representations of these indices arealso determined and stored in vectors x and y as shown. The test in step2415 determines whether j is bigger than 2^(m−1). If so, then there isan error, and the process halts in step 2420. If not, then step 2425tests whether j equals 2^(m−1). If so, then step 2430 checks whetherx_(m) equals 0. If not, then the process halts with an error. If yes,then the process outputs, in step 2440, the vector (x₀, . . . , x_(m−1),0, x₀, . . . , x_(m−1)) comprising 2^(m+1) bits. If the test in step2425 is negative, i.e., if j is less than 2^(m−1), then the processoutputs in step 2435 the vector (x₀, . . . , x_(m), y₀, . . . , y_(m−1))comprising of 2 m+1 bits.

As can be appreciated by those of skill in the art, the processesdescribed in FIGS. 22-24 are simpler than their counterparts in FIGS. 17and 19. For example, it is not necessary to completely sort the inputvector; only the largest and the smallest elements of this vector needto be determined. In a variety of applications, this can be a lotsimpler to accomplish than full sorting.

Many variations of these processes are possible and can be easilyobtained upon a careful study of this enclosure. The descriptions givenare for illustrative purposes only, and are not meant to be limiting.

Examples of Sparse PM Codes

FIG. 25 gives examples of some sparse PM codes according to thedescriptions above. The basic vector corresponding to the PM code is ofthe form shown in Equation 16.

$\begin{matrix}{x_{0} = \left( {a,\underset{n_{1}}{\underset{}{0,0,\ldots \mspace{14mu},0}},{- a}} \right)} & \left( {{Eqn}.\mspace{14mu} 16} \right)\end{matrix}$

In FIG. 25, the first column is the value of n₁, and the second columnis the value of a. The third column is the number of bits that aretransmitted according to the description above, and n is the number ofwires, which is equal to n₁+2. The last column gives the improvement inpower with respect to differential signaling.

Connections with Constant Weight Coding

Another type of coding which has been used in connection withtransmitting signals on a bus of the type presented in FIG. 1 isconstant weight coding. In this coding method, only a given number, d,of the wires carry voltages or currents, while the other n-d do not.Constant weight coding has been studied by a large number ofresearchers. For example [Cornelius] and the references thereindescribes a constant-weight parallel encoding technique which maintainsconstant current in the parallel-encoded data lines and the high and lowpotential driver circuits for the signal lines, and hence can resistvarious forms of switching noise. [Stan-Burelson] and [Tallini] describerelated methods in which a given sequence of bits is transformed into agenerally longer sequence of bits in which only exactly d or at most dbits equal one. Such constant weight coding satisfies Equation 2 above,but does not satisfy Equation 1.

Constant weight coding can be viewed as a special case of PM coding, ifdone properly. For example, it the basic vector x₀ is a vector in whichthe first d coordinates equal some number a (typically equal to 1 inapplications) and the residual n-d coordinates equal some other number b(typically equal to 0 in applications), this can work. In particular,the methods described above can also be used to perform encoding anddecoding operations for constant-weight codes with the basic vectorhaving at least three distinct coordinates (and not two, as is the casein constant-weight coding). This leads to a much larger pin-efficiency,and resistance to many different types of noise to which constant-weightcoding is not resilient.

Multilevel PM Codes

In some cases, one may want to further increase the pin efficiency of acommunication system that builds upon the methods disclosed herein. Away to accomplish this is further explained with reference to FIG. 26.The information source 110 provides a set of d bits to a level modulator2610. In earlier-described embodiments, the permutation encoder 1210would use a basic vector x₀ for the encoding process. In the multilevelPM codes version, this basic vector is supplied by level modulator 2610and this vector is referred to as x₀′. The task of the level modulatoris to modify a basic vector x₀ of a PM code in such a way that the valueof the d bits is embedded into the basic vector. The modified basicvector is sent to the permutation encoder 1310 that performs permutationmodulation encoding based on another set of k bits that is received fromthe information source 110. The way the bits are embedded may depend onthe basic vector x₀ referenced in Equation 10.

In a selected embodiment, the basic vector x₀ has the property that fori≠j we have that a_(i)≠a_(j). In that case, a set S is defined where thenumber of elements of S is given by 2^(d). The level modulator 2710selects one of the elements of S which we denote by s and produces abasic vector x₀′ as shown in Equation 17.

$\begin{matrix}{x_{0}^{\prime} = {s \times \left( {\underset{\underset{n_{0}}{}}{a_{0},\ldots \mspace{14mu},a_{0}}{\underset{\underset{n_{1}}{}}{a_{1},\ldots \mspace{14mu},a_{1}}{\ldots \underset{\underset{n_{t}}{}}{a_{t},\ldots \mspace{14mu},a_{t}}}}} \right)}} & \left( {{Eqn}.\mspace{14mu} 17} \right)\end{matrix}$

One of skill in the art should recognize, from this disclosure, thatEquations 1 and 2 remain valid, which implies that embedding informationin this manner preserves the excellent common-mode rejection propertiesof the scheme. The scheme will incur more SSO noise, but the highernumber of bits that is transmitter per cycle may be more important thanthe increased noise. Furthermore, one of skill in the art will recognizethat for some PM codes, especially, those that are sparse, the problemswith SSO are less severe.

In case there exist indices i and j for which a_(i)=a_(j), the levelmodulator 2710 may produce a basic vector x₀′ from x₀ as shown inEquation 18, where the set S should be chosen in such a way that theordering of the elements of the basic vector remains valid, i.e., thata₀>a₁> . . . >a_(i)> . . . >a_(j)> . . . >a_(t).

$\begin{matrix}{x_{0} = {s \times \left( {\underset{\underset{n_{0}}{}}{a_{0},\ldots \mspace{14mu},a_{0}} {\underset{\underset{n_{1}}{}}{a_{1},\ldots \mspace{14mu},a_{1}}} \left. \quad{\underset{\underset{n_{i}}{}}{{sa}_{i},\ldots \mspace{14mu},{sa}_{i}}{\ldots \mspace{11mu} {\underset{\underset{n_{j}}{}}{{sa}_{j},\ldots \mspace{14mu},{sa}_{j}}}\underset{\underset{n_{t}}{}}{a_{t},\ldots \mspace{14mu},a_{t}}}} \right)} \right.}} & \left( {{Eqn}.\mspace{14mu} 18} \right)\end{matrix}$

It is possible to embed more bits into the PM code by identifyinganother pair of indices k, l for which a_(k)>=−a_(l) and repeating thesame process. The process of embedding more bits into the original PMcode may lead to higher error probabilities. However, to overcome this,the bits supplied by 110 can be encoded with an error-correcting codebefore passing them to the vector signal encoder.

It should be apparent from this description that each of the featuresand/or functions described herein in mathematical terms, such asequations, inequalities, relations and functions, and/or in programmaticterms, such as a sequence of operations, can be implemented in somephysical manner, such as by the use of hardware circuits that effect theoperations represented by those features and/or functions. As such,particular description of specific hardware elements, such as wires,resistors, transistors, active or passive electronic components, is notrequired for a full understanding of the inventions and embodimentsdescribed herein.

Some features and/or functions might be implemented by program code orinstructions executed by a programmable processor or general purposecomputer. However, it should be understood that in some cases, thatwould be impractical. For example, where the communications is over abus between two chips with low power limits and pin constraints, itmight make no sense to spend more power running a programmable processorusing up more power than would be saved relative to a basic chip-to-chipcommunications channel that did none of the operations described herein.

Of course, some operations that can be done ahead of time, such asgenerating tables of values and storing them in memory for repeated use,or configuring an FPGA one time, might be done ahead of time to allowfor the encoding and decoding to proceed efficiently and with lowerpower consumption per transmission period than otherwise. Of course,where chip-to-chip communications are involved, there may also beconstraints on how much chip real estate is available for the encodersand decoders.

In the foregoing specification, the invention has been described withreference to specific embodiments thereof. It will be, however, evidentthat various modifications and changes may be made thereto withoutdeparting from the broader scope and spirit of the invention. Thespecifications and drawings are, accordingly, to be regarded in anillustrative, rather than restrictive, sense.

1-47. (canceled)
 48. An apparatus comprising: a code map unit configuredto receive k source bits as a code map unit input and to generate afirst set of n values where the sum of the squares of the values ispredetermined; a transform unit connected to the code map unit andconfigured to receive the first set of n values and to generate a secondset of n values; and, a modulator configured to generate a modulatedsignal output based on the second set of n values.